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Fundación de Estudios de Economía Aplicada

Visa Policies, Networks and the Cliff at the Border by ** Simone Bertoli^* and Jesús Fernández-Huertas Moraga Documento de Trabajo 2012-12

December 2012

* CERDI, University of Auvergne and CNRS. ** FEDEA and IAE, CSIC.

Jorge Juan, 46 28001 Madrid -España Tel.: +34 914 359 020 Fax: +34 915 779 575 infpub@fedea.es

Simone Bertoli^a and Jesús Fernández-Huertas Moraga^b

^aCERDI^†, University of Auvergne and CNRS ^bFEDEA^‡ and IAE, CSIC

Abstract

The scale of international migration flows depends on moving costs that are, in turn, influenced by host-country policies and by the size of migrant networks at destination. This paper estimates the influence of visa policies and networks upon bilateral migration flows to multiple destinations. We rely on a Poisson pseudo-maximum likelihood estimator to derive estimates that are consistent under more general distributional assumptions on the underlying RUM model than the ones commonly adopted in the literature. We derive bounds for the estimated direct and indirect efects of visa policies and networks that reflect the uncertainty connected to the use of aggregate data, and we show that bilateral migration flows can be highly sensitive to the immigration policies set by other destination countries, an externality that we are able to quantify.

Keywords: international migration, networks, visa policies, multiple destinations, externalities. JEL classification codes: F22, O15, J61.

^∗The authors are grateful to Pedro Albarrán, Michel Beine, Michael Clemens, Frédéric Docquier, Herbert Grubel, Fabio Mariani, Francesc Ortega, C¸ aglar Ozden, Chris Parsons, Giovanni Peri and Hillel Rapoport for their comments, and to the participants in the Eleventh Journées Louis-André Gérard-Varet, in the Fifth Migration and Development Conference, in the VI Workshop on Migration and Labor Economics, in the Second CEPII-OECD Conference on Immigration in OECD Countries, in the XXXVII Simposium of the Spanish Economic Association in Vigo, in the First CEMIR Conference on “International Migration: Competition for Talent and Brain Circulation” in Munich and in seminar presentations at CERDI, at the University of Alicante and at IRES; they are also grateful to Eric Neumayer for making his dataset on bilateral visa policies publicly available; the usual disclaimers apply.

^†Bd. F. Mitterrand, 65, F-63000, Clermont-Ferrand; email: simone.bertoli@udamail.fr.

^‡Jorge Juan, 46, E-28001, Madrid; email: jfernandezhuertas@fedea.es (corresponding author).

“Not only is the world not flat, it is not a curb nor a barrier. Rather, the world has a massive clif at the U.S. border (and, one suspects, most other rich industrial countries have similarly sized clifs).” (Pritchett, 2009, p. 274)

1 Introduction

The share of the world population currently residing outside its country of birth is estimated at around 3 percent (UN Population Division, 2008). It is generally argued that the legal restrictions on cross-border human mobility play a key role in keeping this figure low, as “policy barriers in the destination countries surely play a major role in constraining emigration” (Clemens, 2011, p. 83), and “labor mobility is likely lower than it could be by a factor of between two and five, because it is constrained by host-country policies” (Pritchett, 2006, p. 69).

The policies that exert an influence on the size of migration flows are not only the regulations that shape the legal framework for immigrant admission such as quotas or point-based systems, but they encompass any policy intervention that influences the costs and expected benefits from migration. Policy-induced migration costs create a “clif at the border” (Pritchett, 2009) that hinders the flow of people across countries. Mayda (2010) and Ortega and Peri (2013) provide empirical evidence that an aggregate measure of the restrictiveness of immigration policies reduces incoming flows from all origin countries. Still, some relevant host-country policies are bilateral in nature, so that potential migrants from diferent origins can face diferently sized clifs along the same border.

Visa policies are one part of the legal framework regulating non-immigrant temporary admission at destination and represent a factor that can shape the height of the clif at the border. The requirement of a visa to enter a country can impose substantial costs on travelers, as it forces them to submit an application to the consular ofices of their intended destination, which can ask for processing fees, impose long waiting times, and possibly deny the visa (Neumayer, 2006). A visa waiver allows travelers to move across borders at a substantially lower cost, and with a greatly reduced uncertainty with respect to their admission at destination.¹ This, in turn, suggests that the bilateral visa regime can also influence the scale of migration flows, as it determines the cost of entering legally into the country of destination, and then overstaying there beyond the period for which admission was granted. The US General Accounting Ofice (2004) reports that overstayers amounted to 2.3 million in 2000,² accounting for at least 27 percent of illegal immigrants in the US (US General Accounting Ofice, 2004, p. 10). Six EU member states recently addressed a complaint to the European Commissioner for Home Afairs about the alleged increase in migration inflows from the five Eastern European countries whose citizens had been granted a visa-free access to the Schengen area between 2009 and 2010.³

¹Neumayer (2010) provides evidence on the negative impact of visa requirements on the number of travelers between countries.

Still, the evidence on the influence of the visa regime, and of bilateral immigration policies more in general, upon the scale of international migration flows is limited. Bertoli, Fernández-Huertas Moraga, and Ortega (2011) present descriptive evidence on the role of the visa waivers that Spain used to grant to some of its former colonies in Latin America in determining the size of immigration flows from Ecuador, and Bertoli and Fernández-Huertas Moraga (2013) provide econometric evidence of the influence of changes in visa policies in shaping the size of bilateral flows during the surge of Spanish immigration that began in the late 1990s. Visa waivers exert a positive but only marginally significant efect on migration rates in Grogger and Hanson (2011).⁴

How can we reconcile the perception that destination country policies represent a binding constraint on international migration with the limited empirical evidence on the efects of bilateral policies? Two closely related factors, namely the endogeneity of immigration policies and the dependence of bilateral flows on the attractiveness of other destinations, can explain this puzzle. With respect to visas, Chiswick (1988) observes that “the careful scrutiny given visa applicants, which ofends many foreign students and visitors to the United States, is intended to ferret out those most likely to violate their visas” (p. 104), and the European legislation explicitly refers to the potential for illegal immigration from an origin country as one of the key criteria that is used to determine the visa policy toward its citizens.⁵ Hence, the bilateral visa regime can be correlated with unobservables factors that also shape the scale of migration flows.

²This figure does not include Mexicans who entered with a border crossing card, Canadians or short-term overstays from other countries.

³“L’aflux de migrants des Balkans pr`eoccupe l’Union européenne”, Le Monde, October 24, 2012. The complaint was related to the increase in the number of asylum seekers from these countries, the same reason that also induced Canada to reintroduce in July 2009 the visa requirement on Czech citizens that had been lifted in October 2007, as described by Citizenship and Immigration Canada (source: http://www.cic.gc.ca/english/department/media/backgrounders/2009/2009-07-13a.asp, accessed on December 16, 2012).

⁴Another bilateral policy, the Schengen agreement, is often found to have little to no efect on bilateral migration flows, as in Grogger and Hanson (2011) and Beine, Docquier, and Ozden (2011).

Bilateral visa policies toward a given country are closely correlated across diferent destinations. An article published by The Economist in 2010 reveals that the visa regimes that citizens from diferent origin countries face are highly polarized: holding a passport of a developed country grants visa-free admission (almost) everywhere, while citizens from developing countries need to apply for a visa to be admitted in most destinations around the world.⁶ Such a similarity in the bilateral visa policies toward the citizens of any given country can come from a policy coordination at the supranational level, as it occurs at the EU level,⁷ from a shared perception of the potential for illegal immigration or from the anticipation of an externality due to the policies selected by other countries (Boeri and Br¨ucker, 2005; Giordani and Ruta, 2013).⁸

This feature of bilateral immigration policies implies, as suggested by our initial quote from Pritchett (2009), that “most other rich industrial countries have similarly sized clifs,” and this can create a further key analytical challenge to the identification of their efects due to multilateral resistance to migration (Bertoli and Fernández-Huertas Moraga, 2013). The size of the bilateral migration rate toward a destination depends on the attractiveness of alternative destinations under more general assumptions on the underlying location-decision problem that potential migrants face, and the need to relax restrictive distributional assumptions is created precisely by the diferences in unobservables across countries subject to diferent visa regimes. Such a dependency implies, in turn, that the identification of the efect of the visa regime can be confounded by the visa policies adopted by other countries: potential migrants’ destination choices depend on the relative size of the clifs that characterize diferent borders rather than on their absolute size.

⁵“The determination of those third countries whose nationals are subject to the visa requirement, and those exempt from it, is governed by a considered, case-by-case assessment of a variety of criteria relating inter alia to illegal immigration, public policy and security” (Council Regulation (EC) No 539/2001, March 15, 2001).

⁶“No visa required: Who has more freedom to travel?”, The Economist, August 25, 2010.

⁷The European Council establishes a list of countries whose citizens must be requested a visa to be admitted to any country within the Schengen area; if a country is not on this list, then member states are free to decide whether to grant a visa waiver or impose a visa requirement (Council Regulation (EC) No 539/2001, March 15, 2001).

⁸“Decisions to tighten migration policies may also be driven by policy spillovers across jurisdictions. Migration is a global phenomenon and decisions of a country to close borders may entail substantial diversion of migration flows to another country.” (Boeri and Br¨ucker, 2005, p. 663).

These arguments entail that the limited evidence on the efectiveness of bilateral immigration policies could be related to the confounding influence of the policies adopted in other countries of destination. The contribution of this paper is to propose an econometric approach that is able to identify the efect of bilateral variables on bilateral migration rates while controlling for such a confounding efect in a cross-sectional setting,⁹ while at the same time greatly reducing the concerns related to diferences in unobservables across countries that are subject to diferent visa regimes. In addition, we use our estimates to measure the diversion of the flows to other countries that is produced by the introduction of a visa requirement by one destination. This represents a migration policy externality that we are able to quantify.

We employ a Poisson pseudo-maximum likelihood, PPML, estimator that allows us (i) to be consistent with underlying random utility maximization, RUM, models with diferent patterns of dependency of the bilateral flows on the attractiveness of other destinations (Guimaraes, Figueiredo, and Woodward, 2004; Schmidheiny and Br¨ulhart, 2011), and (ii) to deal with the presence of zeros (Santos Silva and Tenreyro, 2006).

The consistency of the PPML estimator with an underlying RUM model was first established by Guimaraes, Figueiredo, and Woodward (2003), and then extended by Guimaraes, Figueiredo, and Woodward (2004) and Schmidheiny and Br¨ulhart (2011) under more general specifications of the stochastic component of location-specific utility. The RUM-consistency of PPML under diferent specifications of the error term creates, as discussed in Schmidheiny and Br¨ulhart (2011), an uncertainty about the size of the estimated elasticities of bilateral flows with respect to the regressors that had not been considered yet by the international migration literature. Our paper extends Schmidheiny and Br¨ulhart (2011), proposing bounds for the estimated elasticity under a more general specification of the stochastic properties of the underlying theoretical model describing the location-decision problem that potential migrants face.

This paper is related to three diferent strands of literature. First, the literature on the determinants of international migration flows that we reviewed above.¹⁰ Second, the literature on discrete choice models (McFadden, 1974, 1978; Cardell, 1997; Vovsha, 1997; Train, 2003; Wen and Koppelman, 2001; Papola, 2004); third, the papers establishing the consistency of aggregate count data models with individual-level utility maximizing behavior (Guimaraes, Figueiredo, and Woodward, 2003, 2004; Schmidheiny and Br¨ulhart, 2011).

⁹Bertoli and Fernández-Huertas Moraga (2013) propose a more general econometric approach that requires a longitudinal dimension that is often unavailable with international migration data.

¹⁰Other relevant empirical papers include Bratsberg, Dølvik, and Raaum (2012), Clark, Hatton, and

Our econometric analysis draws on the international migration data assembled by Docquier, Lowell, and Marfouk (2009), which we combine with the dataset by Ozden, Parsons, Schif, and Walmsley (2011) to obtain information on the size of the migration networks in 1960, and with the dataset on bilateral visa policies by Neumayer (2006).

The choice of the various specifications of the model to be estimated with PPML are derived from a simple RUM model. The estimates confirm the significant influence of migration networks evidenced by Beine, Docquier, and Ozden (2011), and they also reveal that visa policies play a significant role in shaping the height of the clifs at the border: when the attractiveness of other destinations is properly controlled for, a visa requirement is estimated to reduce the scale of bilateral migration flows between 40 and 47 percent on average. Such an efect is not significant in specifications that are only consistent with more restrictive assumptions on the underlying RUM model, and whose validity is questioned by the tests that we conduct on the residuals. Our results confirm the pressing need to properly control for the confounding influence exerted by the attractiveness of alternative destinations, that is, multilateral resistance to migration.

As far as migration policy externalities are concerned, we estimate that a visa requirement imposed by one destination can increase bilateral migration flows to other destinations from the origin country subject to the visa by between 3 and 17 percent on average. In some particular cases, this externality efect might even be larger than the own-country efect. These results are robust when we estimate our model for each skill group, and we find that low-skill migration flows respond slightly more to changes in visa requirements than high-skill flows.

The rest of the paper is structured as follows: Section 2 develops a simple RUM model that describes the location decision problem that potential migrants face. Section 3 discusses the two main RUM-consistent approaches to the estimation, presenting the arguments that justify our choice to rely on PPML estimation. The data sources and the basic descriptive Williamson (2007), Belot and Hatton (2012), Lewer and den Berg (2008) and McKenzie, Theoharides, and Yang (2012).

statistics are presented in Section 4. Section 5 contains the results from the econometric analysis, and Section 6 draws the main conclusions.

2 A RUM model of international migration

Consider a population of individuals originating from a country , who have to choose their preferred location among the n countries belonging to the set D, including j itself.¹¹ Let represent the scale of the bilateral gross migration flow from country to country and be the vector that collects all the bilateral migration flows originating from country j.We can express as:

\[m _ {j k} = s _ {j} p _ {j k} \eta_ {j k}\tag{1}\]

where is the probability that an individual from country will move to country and is a vector of spatially uncorrelated errors, with for all k.

2.1 Choice probabilities

The n elements of the vector are the outcome of a location decision problem that individuals face, which we describe through a RUM model. Specifically, the utility that the individual i from country j obtains from opting for destination k is given by:

\[U _ {i j k} = V _ {j k} + \epsilon_ {i j k} = \boldsymbol {x} _ {j k} ^ {\prime} \boldsymbol {\beta} + \epsilon_ {i j k}\tag{2}\]

where the deterministic component of utility is a linear function of a vector , and represents an individual-specific stochastic component.The vector that collects the choice probabilities for individual i over the n locations depends on the assumptions about the distribution of the stochastic term. We assume that follows an Extreme Value Type-1 marginal distribution, not independently distributed as in most of the literature but rather positively correlated across destinations; can thus be obtained from a Generalized Extreme Value generating function (McFadden, 1978), as most of the econometric approaches adopted in the literature are all consistent with diferent GEV models.¹²

¹¹We present the RUM model omitting the time dimension of the location decision problem that potential migrants face, but the analysis can be extended to allow for such a dimension.

The need to introduce more general distributional assumptions naturally arises from (i) the presence of unobserved determinants of location-specific utility, and from (ii) the estimation of the determinants of bilateral migration flows on aggregate data.

Imagine, for instance, that cultural proximity between country j and country k, which is unobservable for the econometrician, influences then, a potential migrant from the origin j receives a utility, conditional upon observables, from locating in culturally close (distant) destinations that is systematically higher (lower) than the utility associated to alternative destinations.

The assumption, which we retain from the literature, that the vector of parameters in (2) does not vary across individuals implies that any heterogeneity in the relationship between the elements of and ends up in , introducing correlation in the stochastic component of utility across destinations. Suppose, for instance, that one of the elements of is represented by a dummy variable which signals whether country j and country k share an oficial language. The specification of in (2) implies that the deterministic component of utility that a Belgian would-be migrant obtains from locating in any destination does not depend on whether she is Walloon (French-speaking) or Flemish (Dutch-speaking). This, in turn, implies that the higher (lower) utility that a Walloon (Flemish) receives from locating in any country that has French among its oficial languages introduces a positive correlation in the stochastic component of utility across French-speaking destinations.

This is why the presence of unobservables and the specification of utility in (2) that is adopted in the literature calls for relaxing the assumption that the stochastic component of utility is independently distributed across countries when deriving equations to be estimated on aggregate bilateral migration data.

2.1.1 Distributional assumptions

Let the set of possible locations D be partitioned into m subsets b, also called nests, and let denotes the unique subset to which location k belongs. Nests are groups of countries that share some observed or unobserved characteristics that influence their attractiveness, and whose impact can be heterogeneous across individuals. The individual stochastic component of utility is assumed to be a mixture of a nest-specific and of a location-specific term:¹³

¹²Partial exceptions are also represented by Clark, Hatton, and Williamson (2007) and Mayda (2010) who assume normality of the stochastic component in their theoretical model but then adopt an estimation approach that is consistent with an i.i.d. EVT-1 error term.

\[\epsilon_ {i j k} = (1 - \tau) \nu_ {i j b (k)} + \tau v _ {i j k}\tag{3}\]

where is the weight associated to the location-specific term, and is the unique random variable, whose distribution depends on , that ensures that also follows an EVT-1 marginal distribution (Cardell, 1997).¹⁴ The presence of the nestspecific stochastic component introduces a positive correlation in the realizations of the stochastic component of utility for the locations belonging to the same nest; specifically, we have that , and zero otherwise. The higher the weight associated to the location-specific term, the lower the within-nest correlation of the stochastic component of utility in (2).

2.1.2 The vector of choice probabilities

The element k in the vector of choice probabilities is equal to:

\[p _ {i j k} = \frac {e ^ {\boldsymbol {x} _ {j k} ^ {\prime} \boldsymbol {\beta} / \tau} \Big (\sum_ {l \in b (k)} e ^ {\boldsymbol {x} _ {j l} ^ {\prime} \boldsymbol {\beta} / \tau} \Big) ^ {\tau - 1}}{\sum_ {q} \Big (\sum_ {l \in b _ {q}} e ^ {\boldsymbol {x} _ {j l} ^ {\prime} \boldsymbol {\beta} / \tau} \Big) ^ {\tau}}\tag{4}\]

Averaging over individual decisions, we have that , which in turn allows us to rewrite the element k of the vector of bilateral migration flows as follows:

\[m _ {j k} = s _ {j} \frac {e ^ {\pmb {x} _ {j k} ^ {\prime} \beta / \tau} \Big (\sum_ {l \in b (k)} e ^ {\pmb {x} _ {j l} ^ {\prime} \beta / \tau} \Big) ^ {\tau - 1}}{\sum_ {q} \Big (\sum_ {l \in b _ {q}} e ^ {\pmb {x} _ {j l} ^ {\prime} \beta / \tau} \Big) ^ {\tau}} \eta_ {j k}\tag{5}\]

The assumptions on the stochastic component of location-specific utility in (3) are more general than those adopted by other papers in the literature; specifically, our distributional assumptions reduce to those adopted by Grogger and Hanson (2011) if we further assume that each location belongs to a singleton, i.e. for any Similarly, we can obtain the distributional assumptions in Ortega and Peri (2013), Beine, Docquier, and Ozden (2011) and McKenzie, Theoharides, and Yang (2012) by imposing the restriction that all locations but the origin belong to a unique nest, i.e. and for any . This assumption implies that, conditional upon the deterministic component of location-specific utility, potential migrants regard all possible countries but the origin as being close substitutes, and it can accommodate for diferences in unobservables between migrants and stayers.

€ijk

¹³This specification assumes that ijk contains only one nest-specific variance component; our estimation strategy is actually consistent with multiple nest-specific variance components, which can give rise to an even richer pattern of correlation across destinations (Bertoli and Fernández-Huertas Moraga, 2013).

Vijb(k)

¹⁴The EVT-1 distribution is not self-conjugate, so that the nest-specific term ν_ijb(k) in (3) does not follow an EVT-1 distribution.

The assumptions on the stochastic component that we introduced in (3) allow for a richer pattern of cross-elasticities, as potential migrants can perceive a destination to be a close substitute only for a subset of all the potential destinations, represented by the nest . Specifically, we can use (5) to derive the elasticity of the bilateral migration flow from j to k with respect to the attractiveness of a destination for potential migrants from j:

\[\frac {\partial \ln (m _ {j k})}{\partial \ln (V _ {j l})} = - \Big [ \tau p _ {j k} + (1 - \tau) \frac {p _ {j k} p _ {j b (k)} p _ {j l | b (k)}}{p _ {j l}} \Big ] V _ {j l} / \tau\tag{6}\]

where is the probability that a potential migrant from opts for a destination in the nest , and is the probability of choosing destination l conditional upon opting for the nest 16

If destination , then (6) simplifies to while if the destination l does not belong to the nest , and hence , then the indirect elasticity stands at . As the weight associated to the location-specific stochastic term in (3) lies between 0 and 1, then the indirect elasticity is larger in magnitude when , and it is monotonically decreasing in . Intuitively, the higher the weight associated to the nest-specific stochastic component in (3), the greater the sensitivity of bilateral migration flows to a variation in the attractiveness of another destination within the same nest.

¹⁵An

b(k) = D

alternative equivalent assumption is that for all k ∈ D, as the inclusion of a stochastic k ∈ D component that is common to all locations does not afect the vector of choice probabilities that only depends on the diferences in utility across locations and not on their levels.

j

Vjk

∂ ln(m_jk)/∂ ln(V_jk) = [τ (1 − p_jk) + (1 − τ )(1 − p_jk|b(k))]V_jk/τ .

¹⁷In

Pjl = Pjb(k)Pjl|b(k)

¹⁶The corresponding expression for the direct elasticity of migration flows from j to k with respect to V_jk

this case, we have that pjl = pjb(k)pjl|b(k).

We can rewrite (5) more compactly as follows:

\[m _ {j k} = \exp \left(\alpha_ {j} + \boldsymbol {x} _ {j k} ^ {\prime} \boldsymbol {\beta} / \tau + \gamma_ {j b (k)} + \ln (\eta_ {j k})\right)\tag{7}\]

where the origin specific term is equal to:

\[\alpha_ {j} = \ln (s _ {j}) - \ln \left[ \sum_ {q = 1} ^ {m} \left(\sum_ {l \in b _ {q}} e ^ {\pmb {x} _ {j l ^ {\prime}} \pmb {\beta} / \tau}\right) ^ {\tau} \right]\]

and the origin-nest specific term is given by:

\[\gamma_ {j b (k)} = (\tau - 1) \ln \Big (\sum_ {l \in b (k)} e ^ {\boldsymbol {x} _ {j l} ^ {\prime} \boldsymbol {\beta} / \tau} \Big)\]

Our key interest is to understand whether, and under which hypotheses, we can recover a consistent estimate of the vector of parameters in (2) from the observation of migration flows and of the vector . A key analytical challenge is represented by the correlation between the vector and the term that reflects the attractiveness for potential migrants from of all locations in the nest . If this term is not adequately controlled for, then the ensuing multilateral resistance to migration will determine the endogeneity of all the determinants of location-specific utility in (Bertoli and Fernández-Huertas Moraga, 2013).

3 Two main approaches to the estimation

The estimation of the determinants of bilateral migration flows with aggregate data has to deal with some key analytical challenges, and we focus here on two of them: (i) its consistency with a general underlying RUM model, and (ii) the presence of zero bilateral flows in the data.

We discuss here the two main approaches to the estimation that can be followed, and how they allow to deal with points (i)-(ii) above. The first one, which probably represents the industry-standard in the international migration literature,¹⁸ involves a logarithmic transformation of the bilateral migration rates that can be derived from (5), while the second resorts to non-linear count data models to estimate directly the determinants of the bilateral migration flows described in (5).¹⁹

¹⁸This approach has been adopted, inter alia, by Clark, Hatton, and Williamson (2007), Lewer and den Berg (2008), Ortega and Peri (2013), Mayda (2010), McKenzie, Theoharides, and Yang (2012), Simpson and Sparber (2012), Beine, Docquier, and Ozden (2011), Grogger and Hanson (2011) and Bertoli and Fernández- Huertas Moraga (2013).

3.1 Estimation of bilateral migration rates

The first approach to the estimation adopts the logarithm of the bilateral gross migration rate, i.e. , as the dependent variable. From (5) we have that:

\[y _ {j k} = (\pmb {x} _ {j k} - \pmb {x} _ {j j}) ^ {\prime} \pmb {\beta} / \tau + (\tau - 1) \ln \Big (\sum_ {l \in b (k)} e ^ {\pmb {x} _ {j l} ^ {\prime} \pmb {\beta} / \tau} \Big) + \ln (\eta_ {j k} / \eta_ {j j})\]

which can be more compactly rewritten as follows:

\[y _ {j k} = (\pmb {x} _ {j k} - \pmb {x} _ {j j}) ^ {\prime} \pmb {\beta} / \tau + \varepsilon_ {j k}\tag{8}\]

where:

\[\varepsilon_ {j k} = (\tau - 1) \ln (\gamma_ {j b (k)}) + \ln (\eta_ {j k} / \eta_ {j j})\]

Under the distributional assumptions in (3), depends on the deterministic components of location-specific utility in country k and j and on an error term that is a function of an origin-nest specific term reflecting the expected utility from migration to locations that belong to the same nest as and of a logarithmic transformation of the error term in (5). As discussed in Santos Silva and Tenreyro (2006), the assumption that for any j, k does not sufice to conclude that , as the latter will be, in general, a function of higher-order moments of the distribution of the error term in (5); this, in turn, implies that, if is heteroskedastic with a variance that depends on the regressors in (5), then the error term in (8) will be correlated with the regressors, casting doubts on the unbiasedness of the estimates.

If one assumes that each destination is assigned to a singleton nest, then one can estimate bilateral migration flows as a function of origin and destination characteristics only, as in

¹⁹This approach, which has a long-standing tradition in the internal migration literature, see Flowerdew and Aitkin (1982) for an early application, has been applied by Egger and Radulescu (2009), Beine, Noel, and Ragot (2011), Belot and Ederveen (2012) and Beine and Parsons (2012) in the international migration literature.

Clark, Hatton, and Williamson (2007), Mayda (2010) and Grogger and Hanson (2011).²⁰ Under this assumption, l , so that the equation to be estimated simplifies to:

\[y _ {j k} = (\pmb {x} _ {j k} - \pmb {x} _ {j j}) ^ {\prime} \pmb {\beta} + \ln (\eta_ {j k} / \eta_ {j j})\]

The assumption that the stochastic components follow i.i.d. EVT-1 distributions, so that conditioning upon and sufices to satisfy the independence from irrelevant alternatives, IIA, assumption, allows to recover the vector that appears in the deterministic component of location-specific utility. Still, the appropriateness of this assumption critically hinges on the correct specification of location-specific utility, as omitted variables and heterogeneity across individuals could introduce cross-sectional correlation in the error term.

A first approach that allows to relax the distributional assumptions involves gathering all countries but the origin in a unique nest. Under this assumption, the error term simplifies to:

\[\varepsilon_ {j k} = (\tau - 1) \ln (\gamma_ {j}) + \ln (\eta_ {j k} / \eta_ {j j})\]

where does not vary across destinations. This implies that the inclusion of origin dummies²¹ among the regressors, which was proposed by Ortega and Peri (2013) and adopted in McKenzie, Theoharides, and Yang (2012) and Beine, Docquier, and Ozden (2011), ²² sufices to remove the cross-sectional dependence of the error term, and its correlation with the regressors. This estimation strategy, which is valid under the restrictions on (3) that we just discussed,²³ does not allow to separately identify the value of the vector of coeficients and of the dissimilarity parameter , but just the ratio . The inclusion of the origin-time dummies controls for the component of the error term , where enters separately from . The true value of is unknown but it can be recovered from individuallevel data that allow to estimate the within-nest correlation in the stochastic component of utility, as in Bertoli, Fernández-Huertas Moraga, and Ortega (2013).

²⁰Mayda (2010) includes among the regressors an “atheoretical measure” (p. 1270) of the attractiveness of other locations, represented by the average of GDP per capita.

²¹These dummies have to be interacted with time dummies whenever the data have a longitudinal dimension.

²²McKenzie, Theoharides, and Yang (2012) include origin-time dummies as the focus of their analysis is on the pull factors of Filipino migration, while Beine, Docquier, and Ozden (2011) include origin dummies in a cross-sectional setting to control for “the combined efect of all unobserved characteristics of the origin country” (p. 34) on the bilateral migration rate.

²³McKenzie, Theoharides, and Yang (2012), who estimate the determinants of Filipino migration to 107 destinations between 1998 and 2009, include both (origin)-time and (origin)-destination dummies; their approach is still consistent with the same assumptions on the stochastic term as in Ortega and Peri (2013), though the richer structure of fixed efects increases the plausibility of the underlying distributional assump-

A diferent approach has been adopted by Bertoli and Fernández-Huertas Moraga (2013), who show that longitudinal data allow to estimate (8) under more general distributional assumptions with the adoption of the Common Correlated Efects estimator proposed by Pesaran (2006). Bertoli and Fernández-Huertas Moraga (2013) apply their estimation approach to an administrative monthly dataset: the Estadística de Variaciones Residenciales, which records gross migration inflows to Spain and is characterized by a very low incidence of zeros in the data. This feature of the data allows them to deal with the first analytical challenge discussed above, i.e. the consistency with a general micro-foundation of migration flows, while leaving the second challenge aside.

3.1.1 Interpretation of the estimated coeficients

The inability to separately identify and creates an uncertainty about the elasticity of bilateral migration rates with respect to any of the elements of the vector , as both the direct and the indirect elasticities depend on (see Section 2.1.2). Following the approach adopted in Schmidheiny and Br¨ulhart (2011), we can define bounds for the two elasticities, conditional upon the estimated value of , exploiting their monotonicity in Specifically, computing the direct elasticity for converging to 0 and for , we can observe that:²⁵

\[\left. \frac {\partial \ln (m _ {j k})}{\partial \ln (V _ {j k})} \right| _ {\boldsymbol {\beta} / \tau = \widehat {\boldsymbol {\beta} / \tau}} = \left((1 - p _ {j k | b (k)}) \boldsymbol {x} _ {\boldsymbol {j k}} ^ {\prime} \widehat {\boldsymbol {\beta} / \tau}, (1 - p _ {j k}) \boldsymbol {x} _ {\boldsymbol {j k}} ^ {\prime} \widehat {\boldsymbol {\beta} / \tau} \right]\tag{9}\]

Similarly, with respect to the indirect elasticity, we can define the following interval:

tions.

²⁴Allowing for multiple nest-specific variance components does not afect the proposed bounds, as the correlation across destinations of the stochastic component of utility in this case is positive but lower than the correlation that arises when destinations share just one nest-specific variance component (Papola, 2004).

²⁵Without loss of generality, we have ordered the extremes of the two intervals under the assumption that

\[\left. \frac {\partial \ln (m _ {j k})}{\partial \ln (V _ {j l})} \right| _ {\boldsymbol {\beta} / \tau = \widehat {\boldsymbol {\beta} / \tau}} = \Big (- p _ {j k | b (k)} \boldsymbol {x} _ {\boldsymbol {j k}} ^ {\prime} \widehat {\boldsymbol {\beta} / \tau}, - p _ {j k} \boldsymbol {x} _ {\boldsymbol {j k}} ^ {\prime} \widehat {\boldsymbol {\beta} / \tau} \Big ]\tag{10}\]

The two intervals in (9) and (10) reflect an uncertainty about the true elasticities that cannot be narrowed down by increasing the precision in the estimate of , as this uncertainty arises from the impossibility of separately identifying and

Consider, for instance, the 0.62 estimated coeficient for networks (Beine, Docquier, and Ozden, 2011, p. 37) in the basic specification of the migration equation. As discussed above, this should not be interpreted as the parameter corresponding to networks in (2), but rather as its ratio with respect to the (unknown) as the estimation strategy they adopted is consistent with the presence of a nest-specific variance component.²⁶ According to the data by Docquier, Lowell, and Marfouk (2009), migration flows from Mexico to the US between 1990 and 2000 represented 99.2 percent of total Mexican migration , and approximately 3.5 percent of the population of Mexico-born individuals . From (9), these figures imply that the elasticity of Mexican migration to the US with respect to the local networks of Mexicans ranges between 0.022 and 0.615.²⁷ The range of the possible elasticities that are consistent with the model is not specific to the example we chose, but it just reflects the fact that , which occurs whenever only a small share of the population migrates.

3.1.2 Zero flows in the data

The second dificulty related to the adoption of the logarithm of the bilateral migration rate as the left hand side relates to the fact that the incidence of zeros in migration datasets is, in general, very high. The share of zero observations stands at 9 percent in Grogger and Hanson (2011), 36 percent in Beine, Docquier, and Ozden (2011), 70 percent in Ortega and Peri (2009),²⁸ and up to 95 percent in Simpson and Sparber (2012). Some analyses have been carried out on a sample restricted to non-zero observations only (McKenzie, Theoharides, and Yang, 2012; Grogger and Hanson, 2011; Bertoli and Fernández-Huertas Moraga, 2013). Ortega and Peri (2013) have resorted to a scaled-OLS estimation, while Simpson and Sparber (2012) and Beine, Docquier, and Ozden (2011) have resorted to a threshold Tobit model and to a two-step Heckman selection control procedure respectively. The first two approaches are exposed to the criticism expressed by Santos Silva and Tenreyro (2006).²⁹

D/{j}

k 6= j,

<β

b(k) =

²⁶Specifically, the estimation strategy in Beine, Docquier, and Ozden (2011) is consistent with b(k) = for all and we can use this relationship to simplify (9).

β/τ

27When τ converges to 0, all the elements of βb also needs to be converging to 0 to keep βd/τ unchanged, and this explains that low direct elasticity.

²⁸The figure goes down to 10 percent when Ortega and Peri (2009) use migrant stocks rather than flows as the dependent variable, as Grogger and Hanson (2011) did; bilateral stocks can be regarded as a proxy for the unobserved bilateral gross flows, which is the theoretically relevant measure of migration in a location decision problem.

The threshold Tobit model developed by Eaton and Tamura (1994) was proposed by Martin and Pham (2008) as a superior alternative to the PPML estimation favored by Santos Silva and Tenreyro (2006), but Santos Silva and Tenreyro (2011) have recently questioned the ability of this estimator to deal with a large share of zeros in the data.³⁰

The reliance on a two-step Heckman selection control procedure is confronted with two diferent sorts of dificulties, which relate to the exclusion restriction and to the consistency of the first stage estimation with the structure of the error term in (8). Specifically, finding a variable that, conditional on the other regressors, exerts a significant influence on the probability of observing a positive flow, but that is uncorrelated with the size of the flow once this is positive is a challenging task,³¹ all the more so when the dataset has a longitudinal dimension. A further challenge relates to the consistency of the assumptions on the error term that underlie the second stage equation, and the assumption of normality in the first stage equation. If the second stage equation is characterized by the presence of cross-sectional correlation in the residuals, then also the non-linear observations in the non-linear first stage will not be independent.³² These arguments suggest that further concerns, beyond the doubts cast by Santos Silva and Tenreyro (2006), relate to the chance of satisfactorily dealing with the presence of zeros in the migration data under a general specification on the (unknown) underlying data-generation process.

²⁹“These procedures will generally lead to inconsistent estimators of the parameters of interest. The severity of these inconsistencies will depend on the particular characteristics of the sample and model used, but there is no reason to believe that they will be negligible” (Santos Silva and Tenreyro, 2006, p. 643).

³⁰The Monte Carlo evidence that they provided reveals that the bias associated to the threshold Tobit estimator is large, and close to the one that characterizes the estimation on the truncated sample of positive observations.

³¹Beine, Docquier, and Ozden (2011) rely on bilateral diplomatic representation as an exclusion restriction in a cross-sectional setting.

³²See Fernández-Val and Vella (2011) and Arellano and Bonhomme (2011) for an overview of the challenges connected to the estimation of nonlinear panel models required for the first stage equation.

3.2 Poisson estimation of bilateral migration flows

The estimation approach proposed by Santos Silva and Tenreyro (2006) is precisely meant to deal with the presence of a large share of zeros in the data, and it is gaining momentum in the international migration literature. PPML estimation performs well even when the data are not Poisson-distributed (Santos Silva and Tenreyro, 2011).³³

Hence, we focus here on the consistency of the Poisson estimation with the RUM model underlying the scale of the observed bilateral migration flows. This requires going back to the expression for in (7), which we report here for convenience:

\[m _ {j k} = \exp \left(\alpha_ {j} + \boldsymbol {x} _ {j k} ^ {\prime} \boldsymbol {\beta} / \tau + \gamma_ {j b (k)} + \ln (\eta_ {j k})\right)\]

If one assumes, as before, that for all , that is to say that the IIA assumption holds, then we can simplify the expressions for and , as we have that and . Hence, when IIA characterizes the underlying RUM model, we can rewrite as follows:

\[m _ {j k} = \exp \left(\boldsymbol {x} _ {j k} ^ {\prime} \boldsymbol {\beta} + \ln (s _ {j}) - \ln \left(\sum_ {l \in D} e ^ {\boldsymbol {x} _ {j l} ^ {\prime} \boldsymbol {\beta}}\right) + \ln (\eta_ {j k})\right)\tag{11}\]

Some key observations emerge from the inspection of (11). First, the scale of the bilateral migration flow from to k always depends on the utility associated to all possible destinations, and not only to the utility associated to the origin and the destination k.³⁴

Second, the adoption of the PPML estimator prevents the identification of the efect of the so-called push factors of international migration, as the deterministic component of utility at origin enters into the exponential term in (11) in a non-linear wa y.³⁵

³³This estimation technique produces consistent estimates as long as the conditional mean is correctly specified (Gourieroux, Monfort, and Trognon, 1984).

³⁴This reflects the fact that the assumption that the stochastic component of the RUM model is i.i.d. EVT-1 implies that the bilateral migration rate, not the flow, is independent from the attractiveness of other destinations; even this restrictive distributional assumption allows for the diversion of flows due to changes in the opportunities to migrate to other countries.

V_jj

Mjkt

mjj;

mjj

m_jk/m_jj

m_jk/m_jj

³⁵Observe that enters linearly into the exponential of the ratio of the conditional means for m_jkt and m_jj ; still, the conditional mean of the ratio never coincides with the ratio of the two conditional means (specifically, the conditional mean of is higher than the ratio of the conditional means of m_jk mjk and m_jj by Jensen’s inequality, independently on the distributional assumptions on the underlying datagenerating process), and this, in turn, violates the condition that is required to obtain consistent estimate

Third, a RUM-consistent estimation of (11) requires the inclusion of origin dummies to absorb the efect of population at origin and of the attractiveness of all possible locations upon . The inclusion of origin dummies implies that the expected value of conditional upon and the set of dummies is independent across all observations in the dataset, which represents a necessary condition for the estimation of the Poisson model.

Guimaraes, Figueiredo, and Woodward (2003) demonstrate that the estimation of (11) through PPML delivers the same estimate for as a conditional logit model estimated on individual-level data on the same determinants of location-specific utility, as the loglikelihood functions of the two models are identical up to a constant.³⁶ Hence, this estimation technique is fully consistent with the underlying RUM model that describes the choice of the utility-maximizing location.

Schmidheiny and Br¨ulhart (2011) generalize this result under the same assumptions as in Ortega and Peri (2013), so that the model to be estimated becomes:

\[m _ {j k} = \exp \left(\boldsymbol {x} _ {j k} ^ {\prime} \boldsymbol {\beta} + \ln (s _ {j}) + \tau \ln \left(\sum_ {l \in D} e ^ {\boldsymbol {x} _ {j l} ^ {\prime} \boldsymbol {\beta} / \tau}\right) - \ln \left[ e ^ {\boldsymbol {x} _ {j j} ^ {\prime} \boldsymbol {\beta}} + \left(\sum_ {l \in D / \{j \}} e ^ {\boldsymbol {x} _ {j l} ^ {\prime} \boldsymbol {\beta} / \tau}\right) ^ {\tau} \right] + \ln (\eta_ {j k})\right)\tag{12}\]

PPML estimation of (12) delivers the same estimate for as the estimation of an individual-level nested logit model, with the nest structure that we just described (Schmidheiny and Br¨ulhart, 2011). Observe that the origin fixed efects sufice to restore independence across observations both in (11) and (12), although the stochastic properties of the two underlying RUM models difer.³⁷ This, in turn, implies that PPML estimation is characterized by the same fundamental uncertainty about the magnitude of the elasticity of migration flows as the estimation of the determinants of the bilateral migration rates, which is connected to the inability to identify the dissimilarity parameter . PPML ofers no advantage, in this respect, over the traditional approach to the estimation reviewed above.

with PPML (Gourieroux, Monfort, and Trognon, 1984).

j;

³⁶Guimaraes, Figueiredo, and Woodward (2003) focus on location-decisions taken from a single origin, so that α does not vary with Guimaraes, Figueiredo, and Woodward (2004) show that, with multiple time periods, the inclusion of origin-time dummies sufices to restore the parallel between the conditional logit and Poisson.

D/{j}

³⁷The key is that the term describing the expected utility from migration to any destination in the nest does not vary across destinations, so that it is absorbed by the origin fixed efect, which is always to be included in the estimation (Guimaraes, Figueiredo, and Woodward, 2004).

3.2.1 Consistency with RUM under less restrictive distributional assumptions

Schmidheiny and Br¨ulhart (2011) established the consistency of the PPML estimation with an utility-maximizing behavior of the migrants under the same assumption on the stochastic properties of the RUM model used in Ortega and Peri (2013). Here, we go one step further, showing that the same consistency characterizes the estimation of (7), which we derived from (3). We reproduce here (7):

\[m _ {j k} = \exp \left(\alpha_ {j} + \boldsymbol {x} _ {j k} ^ {\prime} \boldsymbol {\beta} / \tau + \gamma_ {j b (k)} + \ln (\eta_ {j k})\right)\]

PPML estimation requires observations to be cross-sectionally independent and, as discussed in Guimaraes, Figueiredo, and Woodward (2004), this can be achieved with the inclusion of a richer structure of dummies. Specifically, the inclusion of origin-nest dummies sufices to control for γ , and restore cross-sectional independence of the residuals.³⁸ This, in turn, will produce a consistent estimate of , which is identified only out of within-nest variation.

Such an approach requires to specify the assumptions on the nests and it is feasible thanks to the absence of an incidental parameter problem in the estimation of a Poisson model (Trivedi and Munkin, 2010). The estimation delivers the same estimate for as the individual-level estimation of a nested logit model with location-specific regressors.

The choice of nests b is a data-dependent empirical exercise with a clear trade-of. As the number of nests used to specify equation (7) increases, the available variability that can be exploited to estimate goes down. On the other hand, choosing a too parsimonious specification with few nests may not be able to fully restore the cross-sectional independence of the residuals that is needed to be able to interpret the coeficients of the model as coming from a RUM framework. In able to assess this trade-of, the next subsection introduces a test of the cross-sectional dependence of the residuals in equation (7).

3.2.2 Tests for spatial dependence of the residuals

The spatial independence of the migration flows from a given origin to diferent destinations can be assessed through tests on the residuals generated by the various specifications of our estimates. Specifically, let represent the Pearson residual associated to the migration flow from the origin to the destination and be the vector of Pearson residuals for destination k. If the set of fixed efects introduced among the regressors sufices to restore spatial independence, then we should have , while the presence of a nest-specific stochastic component of utility would entail that As the RUM model gives us an expectation on the direction of the correlation if we do not have cross-sectional independence, we can adapt a modified version of the CD test proposed by Pesaran (2004).⁴⁰ Let denote the correlation between the vectors and the CD test statistic is given by:

³⁸A similar use of nests can be found in the analysis of firms’ location choice by Head, Ries, and Swenson (1995) and Levinson (1996); see also the other papers cited by Guimaraes, Figueiredo, and Woodward (2004).

\[C D = \left(\frac {2 n _ {o}}{n _ {d} (n _ {d} - 1)}\right) ^ {1 / 2} \sum_ {k = 1} ^ {n _ {d} - 1} \sum_ {l = k + 1} ^ {n _ {d}} \widehat {\rho} _ {k l}\tag{13}\]

where and represent respectively the number of origins and destinations in the dataset. Under the null of no cross-sectional correlation in the residuals, the CD test statistic is asymptotically distributed as a standard Normal variable.

In the empirical part of the paper, we will use the CD statistic to choose a model that is parsimonious enough while being able to restore the cross-sectional independence of the residuals in equation (7).

4 Data

4.1 Data sources

We draw our data from three main sources. The first one is represented by Docquier, Lowell, and Marfouk (2009), who provide information on the size of bilateral migration stocks in 31 countries of destination in 1990 and 2000. This dataset provides a proxy for the scale of bilateral gross migration flows that is represented by the variation in stocks,⁴¹ that has been used, inter alia, by Beine, Docquier, and Ozden (2011). In fact, our objective is to start by replicating the results in Beine, Docquier, and Ozden (2011) so as to make our methodology directly comparable with a well-known paper in the literature. Bilateral migrant stocks are defined on the basis of country of birth for all but five destinations (Germany, Hungary, Italy, Japan and Korea), which resort to citizenship to identify immigrants. This dataset is matched with the one assembled by Ozden, Parsons, Schif, and Walmsley (2011), giving us the size of bilateral migration stocks in 1960, which will be used as an instrument for the size of networks in 1990.

³⁹Hsiao, Pesaran, and Pick (2012) provide evidence on the reliability of the Pearson residuals when testing for cross-sectional dependence in non-linear models.

⁴⁰“The choice of the appropriate test should be supported by a priori information (e.g. from economic theory) on the way statistical units may be correlated” (Moscone and Tosetti, 2009, p. 558), and this is why we are not concerned here with the fact that the CD test might fail to reject the null of cross-sectional independence when the data present both patterns of positive and negative correlation (Frees, 1995).

With respect to bilateral visa policies, we use the dataset by Neumayer (2006), which is based on the Travel Information Manual, a yearly publication of the International Air Transport Association, IATA. The Travel Information Manual contains information on all the legal requirements related to transit or non-immigration admission into all countries of the world, including visa requirements. Neumayer (2006) built a dichotomous variable signaling whether the citizens of country j are requested to have a visa for entering into country k or they benefit from a visa waiver.⁴² Observe that visa policies are based on citizenship rather than on country of birth, which is the basis for most of the migration data used in our analysis; the measurement error induced by this discrepancy is likely to be negligible as citizenship and country of birth are likely to coincide for the vast majority of the population in each origin country. This dataset, which has been used also in Neumayer (2010, 2011), refers to the year 2004. As we will be using the information contained in this dataset to estimate the determinants of migration flows between 1990 and 2000, this introduces an additional source of measurement error related to the changes in visa policies that might have occurred between our period of analysis and 2004, but “this measurement error is small because the number of changes to visa restrictions is likely to be very small compared to the total number of restrictions in place” (Neumayer, 2010, p. 173).^{43 44}

⁴¹This is a common practice in the migration literature, which implies that “it is impossible to know how exactly these changes balance attrition (and whether attrition is caused by death, return migration or emigration to a third country) and new entry flows.” (Docquier and Rapoport, 2012, p. 725).

⁴²Visas that need not to be requested before traveling are considered as visa waivers, as a visa that can be obtained upon arrival “typically does not represent any restriction at all because the procedure of getting it is extremely simple and does not involve any major check on the applicant.” (Neumayer, 2010, p. 173).

We also draw on Mayer and Zignago (2011) for the time-invariant dyadic variables such as distance, common language, colonial relationship and contiguity, which can influence bilateral migration costs.

4.2 Descriptive statistics

Table 1 presents the summary statistics for the variables that will be used in the estimation below. The first panel presents the full dataset of 31-destinations-times-182-origins dyads while the second focuses on those observations for which the variation in bilateral migration stocks between 1990 and 2000 takes strictly positive values. The sample size goes down from 5,611 origin-destination observations⁴⁵ to just 3,466, fully dropping three destinations: Hungary, Korea and Poland.⁴⁶ Thus, 62 percent of the observations remain for OLS regressions on the logarithm of the bilateral migration rate. The largest increase in the bilateral stock (3.7 million) corresponds to the Mexican migration to the US whereas the minimum (-189,660) refers to the decline of the stock of German migrants in the US. Incidentally, only 7 percent of the observations take negative values, which means that the share of strict zeros is 31 percent. The average value is less than 3,000 immigrants per origin-destination pair in the total sample and it goes up to more than 5,000 immigrants in the strictly positive sample. The standard deviations are in both cases notably larger than the means (52,910 and 66,991 respectively), pointing out to a high level of dispersion in the data.

The first independent variable in Table 1 is the size of migration networks for each origindestination pair in the year 1990. The average in this case is over 7,000 immigrants with a maximum of 2.7 million corresponding again to the Mexican network in the US. On the lower end, up to one third of the sample corresponds to zero values in the first panel, number reduced to just 6 percent in the lower panel. Some of the regressions in the Appendix also use the 1960 size of the networks. In this case, the average is lower (5,867 immigrants) although the maximum is still quite high, corresponding this time to the 2.2 million Polish-origin individuals living in Germany. The number of zeros in this variable is 35 percent in the full sample and 21 percent in the lower panel.

⁴³We can also observe that a similar measurement error occurs in Grogger and Hanson (2011), who include the bilateral visa policies in 1999 among the determinants of the size of bilateral migration stocks in 2000.

⁴⁴We have rerun our analysis on the data on gross migration flows to 15 of our destinations for 2005 and 2006 by Ortega and Peri (2013) in order to fully address the concerns related to this type of measurement error in the visa variable.

⁴⁵The sample does not include the 31 dyads for which the origin and the destination country coincide.

⁴⁶The size of the 1990 migrant stock are estimated rather than observed for 10 destination countries, including Hungary, Korea and Poland (Docquier, Lowell, and Marfouk, 2009, p. 317), and this introduces a measurement error in the variable; more specifically, the size of the estimated stocks for these three destinations are lower, for all origin countries, than observed stocks in 2000.

Next, the dummy variable representing the visa requirement to enter a given destination from a given origin has an average value of 0.69 in the full sample and a slightly lower 0.67 in the lower panel. Thus, its variability does not hinge on the inclusion of zero-flow observations in the sample. These figures suggest, that, on average, the citizens of the origin countries in our sample require a visa to be admitted in 69 percent of the destinations; this average hides a considerable variability across origins, as revealed by Figure 1. As mentioned in the introduction, the opportunities for non-immigrant admission at destination are highly polarized, with 64 countries facing a visa requirement in all countries in our sample, and 13 countries benefiting from a visa waiver in all destinations.

The following variable in Table 1 refers to the Schengen treaty. It takes value 1 when both the origin and the destination country belonged to the Schengen area at some point in the 1990s and 0 otherwise. The members of the Schengen area (nine of the 31 destination countries in this period) adopted a common visa policy toward any origin country in our sample in 2004,⁴⁷ so that the inclusion of this variable, which is introduced following the main specification in Beine, Docquier, and Ozden (2011), could, if anything, limit the ability of the models below to identify the efect of the visa variable.⁴⁸ Finally, three other classical variables from the literature are presented: colonial links, the existence of a common language and the distance in kilometers between each origin and each destination. None of the three appears very diferent in the two samples.

5 Estimation results

We present first the estimates of the various specifications that we run, and we then discuss the interpretation of the coeficients following the lines proposed in Section 3.

⁴⁷This was not the case in earlier years; for instance, Spain granted a visa waiver to Colombians up to 2001 and to Ecuadorians up to 2003, when a visa requirement was imposed by the European Council regulation (Bertoli and Fernández-Huertas Moraga, 2013).

⁴⁸In fact, the results below are not sensitive to the exclusion of the Schengen variable.

5.1 Estimates

This section presents the results from estimating several versions of the model introduced in Section 2, following some of the diferent strategies presented in Section 3. In order to closely tie the results to the existing literature, we begin by reproducing the OLS estimation in Beine, Docquier, and Ozden (2011) in the first data column in Table 2. The specification is exactly the same as in Beine, Docquier, and Ozden (2011) but for the addition of the visa requirement variable introduced in the previous section. It includes both origin and destination country dummies. The inclusion of origin dummies sufices to make the estimates consistent with an underlying RUM model as in Ortega and Peri (2013), and it controls for all origin-specific push factors of bilateral migration flows. The inclusion of destination dummies absorbs destination-specific pull factors and general immigration policies as those considered by Mayda (2010). Hence, the structure of dummies included among the regressors entails that we can only identify the efects of dyadic variables, with migration networks and bilateral visa policies representing the two key variables of interest.⁴⁹

Reassuringly, this specification produces the same results as in Beine, Docquier, and Ozden (2011) for all of the variables that they also included. Distance, colonial links and common language appear as significant correlates of the log of immigration rates. In particular, the coeficient on the log of networks in 1990 exactly coincides with that in Beine, Docquier, and Ozden (2011): a highly significant 0.62. The introduction of the visa require- ment variable as an additional explanatory variable does not have any efect on the rest of parameters, and the variable itself shows as non-significant.

Section 3 described how the estimation of the OLS model sufers from two key limitations. The first relates to the possible inconsistency with the assumptions on the stochastic component of location-specific utility in the underlying RUM model. If the vector of regressors , which we augmented with the inclusion of bilateral visa policies, fails to include all relevant dyadic determinants of migration or if some observed factors have an heterogeneous impact across potential migrants, then this would introduce correlation between the realizations of the stochastic component of location-specific utility. This, in turn, would give rise to multilateral resistance to migration (Bertoli and Fernández-Huertas Moraga, 2013), with the elements of being correlated with the error term, and with the bilateral migration rate between j and k being still dependent on the attractiveness of destinations other than k. While in principle one could address this concern by testing whether the residuals are characterized by cross-sectional dependence, the highly unbalanced structure of the dataset, which is caused by the exclusion of observations with non-positive flows, hinders the adoption of these tests.⁵⁰

⁴⁹We follow Beine, Docquier, and Ozden (2011) in adding one to the size of the 1990 migration networks so as not to discard zero observations.

The second key problem with the OLS specification is precisely the need to discard nonpositive values,⁵¹ which can bias the estimated coeficients (Santos Silva and Tenreyro, 2006). This problem can be directly dealt with by using the Poisson regression model on the full sample from Table 1.⁵² Specification (2) in Table 2 shows the result from running a Poisson regression on exactly the same variables as in specification (1).⁵³ The estimates in specifications (1) and (2) are very similar,⁵⁴ with just two minor changes. PPML estimation makes the colonial variable become insignificant whereas the Schengen variable turns marginally significant. The visa requirement variable is still insignificant in this specification.

The RUM-consistency of the Poisson estimates depends, as discussed in Section 3, on the absence of cross-sectional dependence in the error term. The presence of cross-sectional dependence in the residuals would imply that the coeficients from specification (2) cannot be interpreted as being consistent with the underlying RUM model. In this case, they should be rather seen as the outcome of an atheoretical specification. To check whether this is the case, we computed the CD statistic for specification (2). Table 2 shows a statistic of 17.35,⁵⁵ which strongly rejects the null of cross-sectional independence.

⁵⁰See De Hoyos and Sarafidis (2006).

⁵¹We also estimated the model with scaled-OLS. The coeficient of the visa variable is insignificant also in this case. Results available from the authors upon request.

⁵²For the purposes of estimation, the 7 percent of negative values are set to zero, as variations in bilateral stocks are used as a proxy for unobserved gross flows, which are always nonnegative.

⁵³As discussed in Section 3, the inclusion of origin dummies is a necessary, though not suficient, condition to restore the independence across observations (Guimaraes, Figueiredo, and Woodward, 2004), and it also implies that the consistency of the estimates does not hinge upon the stochastic component of the RUM model being i.i.d. EVT-1 (Schmidheiny and Br¨ulhart, 2011).

⁵⁴We report robust standard errors for specification (2), which, as demonstrated by Gourieroux, Monfort, and Trognon (1984), make the estimates from the Poisson regression consistent even when the data are not characterized by the equality between mean and variance; the test on the residuals proposed by Cameron and Trivedi (2010) reveals that the equi-dispersion property is indeed not satisfied by our model.

⁵⁵We calculate the tests with the xtcd command in Stata, introduced by Eberhardt (2011).

5.1.1 Reducing cross-sectional dependence

The alternative approach that we adopt here is to restore cross-sectional independence by reducing the variability in the data that is used for identification. Specifically, as discussed in Section 3.2.1, the inclusion of origin-nest dummies allows us to control for unobservable nestspecific components of location-specific utility that have a diferential impact on potential migrants from diferent countries of origin.⁵⁶ This approach is much less demanding in terms of data requirements, but it needs to specify assumptions about the composition of the nests of destinations that share unobserved components of location-specific utility.⁵⁷

While the composition of the nests is necessarily arbitrary, its adequacy can still be measured through its ability to restore the spatial independence of the residuals of the model. There is a clear trade-of between the fineness of the nests and the loss of identification power. Coarser nests, with the unique nest of destinations `a la Ortega and Peri (2013) representing the limiting case of coarseness, have more identification power at the expense of a greater risk of an incorrect specification. Finer nests, like the ones presented here, run the risk of saturating the model and losing much of the identification power in the data. In the limit, the finest partition, which is represented by single-destination nests, ensures cross-sectional independence but delivers no identification in the cross section as they would be equivalent to origin-destination fixed efects.

This trade-of suggested the following approach: if the CD test rejects the null of crosssectional independence on the basis of a specification with nests, then we opt for a specification with nests. This requires us to determine the criteria that inform how we define finer nests, and we opted for geographical proximity of the destinations and income per capita as the two guiding factors. We stop once the nest structure produces residuals that do not lead to the rejection, at conventional confidence levels, of the null hypothesis of cross-sectional independence.

As the CD test conducted on the residuals from specification (2) in Table 2 where rejected the null, we opted for a specification with two nests, the nest including Europe and the nest including all the other destinations. This specification reduced the CD test to 5.52, but it still leads to reject the null of cross-sectional independence at the 1 percent confidence level. We then divided the nest into a nest containing high-income countries (Australia, Canada, Japan, New Zealand and the US), and a nest for emerging countries (Korea, Mexico, South Africa and Turkey). This specification with generated a CD statistic of 3.92, still rejecting at the 1 percent confidence level. The following step was to split the nest between a nest for North America (Canada and the US) and a nest for the other countries, but this only reduced the value of the CD test to 3.82 (p-value of 0.000). We then divided the large European nest between the nest for Western European countries and a nest for Eastern European countries. The value of the CD statistic went further down with this five-nest specification to 3.30, but it sill rejected the null at the 1 percent confidence level.⁵⁸

⁵⁶Cultural proximity might be, as discussed above, one of these unobservables; a nest of destinations that share similar cultural traits would be attractive (unattractive) for potential migrants from origin countries with a culture that is close (distant) from the one of that nest of destinations.

⁵⁷See, for instance, the discussion on the composition of the nests in Head, Ries, and Swenson (1995), p. 241.

Finally, we ran a six-nests specification, further dividing the Western European nest into a nest for the EU-15 countries, and a nest for the three members of the European Free Trade Association, namely Iceland, Norway and Switzerland. Here we stopped, as the residuals generated from this specification of the model no longer led to a rejection of the null. Specification (3) in Table 2 reports the estimates,⁵⁹ obtained interacting the origin dummies with the nest dummies, so that the coeficients are identified only out of within-nest variability in the data.

As discussed above, this identification strategy works under the assumption that the unobserved components of location-specific utility that induce a cross-sectional correlation in the error term are nest-specific, with the destinations belonging to any of the six nests regarded as close substitutes by potential migrants. Their location choices within each nest are more sensitive than the decision to migrate to variations in the attractiveness of any other destinations in the nest.

The loss of identification power is reflected in the lack of precision in the estimates ⁵⁸Auxiliary regressions are available from the authors upon request.

b₁₁₁

b₂₁₁

b₁₁₂

b₂₁₂

⁵⁹The origin dummies are interacted with the following six nests: (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden and the United Kingdom), (Iceland, Norway and Switzerland), (Czech Republic, Hungary, Poland and b₁₂ Slovakia), (Canada and the US), (Australia, Japan and New Zealand) and b (Korea, Mexico, 22 South Africa, and Turkey). Notice that our estimation approach does not require that other destinations that are not included in our sample do not belong to these six nests. For instance, Romania could belong to the Eastern European nest b₁₂, or Brazil could belong to the nest of emerging countries. b12 b₂₂

for the Schengen and distance variables.⁶⁰ On the other hand, the colonial and common language variables become marginally significant. The migration networks variable remains highly significant although the value of the coeficient falls in this specification: 0.567. This fall is what we could expect from the existence of a problem of multilateral resistance to migration that is addressed by the use of the appropriate nest structure. The reason is that a larger network from one origin to a particular destination will be typically correlated with lower networks to destinations that are perceived as substitutes. In a specification, such as (1) and (2) in Table 2, that does not control for multilateral resistance to migration, the network variable might be picking up the own larger network efect together with the other destinations lower network efects, leading to an upward bias in the coeficient, which appears to be limited in this case.

Still, the most notable change in specification (3) in Table 2 relates to the coeficient of the visa variable, which turns highly significant with a value of -0.667. The economic interpretation of the observed change is clear: visa policies toward any origin are closely correlated across several destinations, as evidenced by Figure 1, and this, in turn, introduces a correlation between the bilateral visa policy adopted by country k and the attractiveness of alternative destinations for potential migrants from country j. Once we account for the attractiveness of alternative destinations through the inclusion of origin-nest dummies, bilateral visa policies become significant determinants of the scale of bilateral migration flows. This change in the estimated efect of visa policies once multilateral resistance to migration is controlled for is in line with the results found by Bertoli and Fernández-Huertas Moraga (2013) for Spain.

Are the results in specification (3) preferable to those in specification (2) in terms of their RUM-consistency? They are, since the CD test performed on the residuals from specification (3) does not, by construction, reject the null of spatial independence, as the value of the statistic stands at -1.57 (p-value of 0.117). The much larger value of the log pseudo likelihood function with respect to specification (2) also represents another reason to favor specification (3), as pointed out by Guimaraes, Figueiredo, and Woodward (2004). A remaining threat to identification would be represented by the existence of diferences in dyadic unobservables within a nest. For example, in the presence of reverse causality, with destinations requiring visas whenever migration flows from an origin are high, we would expect the magnitude (in absolute value) of our coeficient to be downward biased. Bertoli and Fernández-Huertas Moraga (2013), who can control for time-varying dyadic unobservables thanks to the frequency and to the longitudinal dimension of their data, find a larger efect of visa policies on migration flows to Spain. This might suggest that our estimate of the visa efect might indeed be downward biased, though our estimation approach already greatly reduces the concerns related to unobservables, accounting for their influence on the pattern of correlation in the stochastic component of utility. The existence of a credible instrument for visa policies would help to dismiss this residual concern.⁶¹ Still, our analysis has shown that controlling for multilateral resistance to migration is already able to unveil a large and highly significant efect that more traditional estimation approaches fail to reveal.

⁶⁰The instability of the estimated coeficient for distance is not related to its correlation with the visa variable. Although the raw correlation between the two stands at 0.25, suggesting that distance to the destination country is positively correlated with the imposition of a visa requirement, this correlation declines to 0.04 once we partial out origin and destination fixed efects and to 0.03 after partialling out origin-nest fixed efects, so that multicollinearity cannot explain the change in the significance of distance.

5.2 Uncertainty on the elasticities

Once we have an estimation technique that is well micro-founded and thus consistent with the theory, such as the one presented in specification (3) in Table 2, our objective is to provide an economic interpretation of the estimates. However, we have seen in Section 3 how none of the presented techniques allows us to escape from a fundamental uncertainty on the calculation of the elasticities implied by the theoretical model. The reason is that Table 2 gives us estimates for whereas we are unable to separately identify the elements of the vector and This subsection provides the empirical counterpart of 3.1.1 and 3.2.1, calculating the elasticity bounds implied by this fundamental uncertainty for the RUM model. We concentrate on the two key variables of interest, migration networks and the visa requirement, using the estimates from specification (3) in Table 2.

5.2.1 Network elasticities

Calculating the bounds of the elasticity of migration flows with respect to the size of the networks is a straightforward task. We just need to follow equations (9) and (10) for the direct and indirect elasticity respectively. The summary statistics for the upper and lower bound of this direct elasticity can be observed in the upper panel of Table 3,⁶² while each dot in Figure 2 represents the two bounds for an origin-destination dyad. Since we chose to represent the lower bounds in the horizontal axis, this implies automatically that all the observations are above the 45 degree line. The figure shows how the upper bound tends to be quite similar for most countries. The reason is that the upper bound depends on unconditional probabilities of emigration which, for most countries, count for a fairly small share of the total population. On the contrary, the lower bound depends on conditional probabilities of migration within the nest which, for many countries, are bound to be quite substantial (e.g., Mexican migration to the US). All in all, Table 3 shows that the average upper bound is 0.57, with this figure coinciding with the estimated coeficient. On the other extreme, under a high correlation in the unobserved component of utility between destinations of the same nest, the average lower bound for the elasticity of migration with respect to networks would stand at 0.46.

⁶¹The result on the visa variable in our preferred specification is robust when we use as a dependent variable the gross migration flows for 15 of our destinations for 2005 and 2006 in the dataset by Ortega and Peri (2013). Results are available from the authors upon request.

The heterogeneity of the results does not stop at the direct elasticities. Our simple RUM migration model also has implications for the cross-elasticity. Equation (10) generates the bounds for the cross-elasticity that has typically been absent from the literature:⁶³ the elasticity of the migration flow from the origin j to the destination k with respect to the migration networks of j in another country . The upper panel of Table 3 presents the averages of the upper and lower bound for this cross-elasticity, while Figure 3 represents the clouds of dyad-specific cross-elasticities.⁶⁴ The average upper bound for the cross-elasticity is almost zero.⁶⁵ As for the lower bound, which corresponds to the largest within-nest correlation, the the average cross-elasticity is higher in absolute value: -0.11.⁶⁶

⁶²The averages of the various bounds are virtually unafected if we resort to an unweighted averaging.

⁶³Bertoli, Fernández-Huertas Moraga, and Ortega (2013) represent an exception in this respect.

l ∈ b(k),

⁶⁴Observe that (10) does not vary with so that we have the same number of direct and crosselasticities.

⁶⁵Remember that the upper bound corresponds to an i.i.d. EVT-1 stochastic term, so this would imply an exact zero if we were looking at the cross-elasticity of migration rates instead of that of flows.

⁶⁶Notice that, logically, the instances of very large (in absolute value) lower bound cross-elasticities correspond to instances of very low lower bound direct elasticities, as the diference between (9) and (10) is independent from τ. For instance, the lowest upper bounds in Figures 2 and 3 correspond both to the Grenada-US dyad, and the diference between the upper bounds for any pair of points that correspond to any origin-destination dyads in the two figures is always 0.567, which corresponds to the estimated coeficient for networks in Table 2.

5.2.2 Visa efects

Diferently from networks, the visa variable is dichotomous, so that we adjusted the formulas presented in Section 3 to account for the discrete nature of this variable, as shown in the Appendix A. The bottom panel of Table 3 presents the averages of these efects implied by the point estimates taken out of specification (3) in Table 2.

The most remarkable aspect that deserves to be commented about the direct and indirect efects of visas is their magnitude. The average bounds mean that we can expect the imposition of a visa requirement by country k on country j to correlate with a decrease of 40 to 47 percent of the level of migration flows from j to k with respect to the level that prevails when a visa waiver is applied.⁶⁷ We can recall from the Introduction that Pritchett (2006) argued that host-country policies could be decreasing migration flows by a factor of two to five; Table 3 shows is that visas might be a big part of that “clif at the border,” being able to almost halve migration flows by themselves.

As it was the case with network elasticities, there is a great deal of heterogeneity in the visa efects. The full extent of this heterogeneity can be observed in Figure 4, which represents the whole range of visa efects calculated for each origin-destination pair. The concentration of points in the lower part of the triangle explains the relatively high level of the visa efect bounds (in absolute value).

The requirement of a visa from country k to the citizens of country j also has efects on the migration flows going to alternative destinations, that is, it creates an externality. The bottom panel of Table 3 presents the average values that quantify this externality whereas Figure 5 represents all of the visa cross-efects bounds for each origin-destination dyad. As in the previous section, the cross-efects are the inverse image of the direct efects. The magnitude of the average bounds ranges between 3 and 17 percent, describing the size of the increase in migration flows from j to l generated by the imposition of a visa requirement by a third country k upon the citizens of j. To our knowledge, these calculated bounds represent the first measure of the possible magnitude of migration policy externalities, that is, the efect of the migration policy of one destination on the migration flows going to another destination. The implication is that countries whose visa policies may have a small efect on the migration flows going out of a particular country may, on the contrary, generate large efects on the migration flows from that particular country to an alternative destination.

⁶⁷Bertoli and Fernández-Huertas Moraga (2013) estimate that the introduction of a visa requirement reduces bilateral migration flows to Spain by up to 76 percent.

For instance, consider Canada, which received little more than 12,000 migrants from Mexico; our estimates suggest that this bilateral flow is highly sensitive to the policies adopted in the US, which represent the largest destination for Mexican migrants. The estimated indirect efect of the US visa policy on Mexicans upon the migration flow from Mexico to Canada range between 90 and 91 percent of the actual flow. This figure is much larger than the direct efect of the Canadian visa policy toward Mexicans, which is estimated at minus 48 percent: hence, the flow of Mexicans to Canada would respond less to a change in the Canadian visa policy than to a change in the US visa policy toward Mexicans.

5.3 Robustness

This subsection presents two types of robustness analysis on the main results presented in specification (3) of Table 2. First, we re-estimate the models with diferent samples. Second, we redefine the dependent variable in order to study low and high-skill migration. For a third type of robustness analysis, we refer the reader to the Appendix B, where we discuss the potential endogeneity problem related to the inclusion of the networks variable.

5.3.1 Diferent samples

The results from Table 2 do not depend on the particular coverage of the dataset described in Table 1. Table 4 reruns specifications (2) and (3) from Table 2 while restricting the sample in two diferent ways: by population size and by income level.

In terms of population size, the objective of the exercise is to guarantee that the main results are not driven by the inclusion of very small origin countries in the sample. To this end, we drop observations with origin countries whose population is lower than one million inhabitants in 1990. With this, the sample size goes down from 5,611 to 4,497 dyads but the main results are virtually unafected, as it can be observed in specifications (1) and (2) from Table 4. Specification (1) does not include origin-nest fixed efects and the Pesaran CD test shows that the residuals could be cross-sectionally correlated. The statistic is 15.55 (p-value of 0.000). The appropriate structure of the residuals is obtained in specification (2), where the CD statistic is -1.89 (p-value of 0.059). If anything, we can observe a larger coeficient for the visa requirement than that presented in Table 2.

We can also restrict the sample by income level, so that we focus more particularly in South-North migration. We do this in specifications (3) and (4) by dropping high-income OECD countries from the set of origins.⁶⁸ We are then left with 4,708 observations. Again, we reject the cross-sectional independence of the residuals in specification (3) where we do not include origin-nest fixed efects. In specification (4), where we include them, the value of the CD statistic is -1.55 (p-value of 0.121) so that we can be confident that we have been able to restore cross-sectional independence and we can interpret the results as coming from a RUM model. In this case, the coeficient on the networks variable is slightly higher while the coeficient on the visa variable is smaller in magnitude than in the baseline specification from Table 2. Still, these diferences are not statistically significant. We can also observe that the distance variable regains significance in this smaller sample.

5.3.2 Estimation by skill levels

In this part, we take advantage from the fact that the dataset by Docquier, Lowell, and Marfouk (2009) allows us to compute migration flows (and rates) by skill level. We define the tertiary educated in their dataset as high-skill whereas the primary and secondary educated are grouped together as low-skill. Table 5 re-estimates the model with and without originnest fixed efects for both high- and low-skill versions of the dependent variable.

Starting with high-skill migration, specifications (1) and (2) confirm that the visa requirement variable only becomes significant once the opportunities to migrate to alternative destinations are taken into account, so that multilateral resistance to migration is controlled for. As before, we can disregard specification (1) on the basis of the CD test, clearly rejected with a statistic of 19.91.⁶⁹ In this case, specification (2) is on the verge of rejecting the null (p-value of 0.050) but we can still have some confidence that this specification has less problems of cross-sectional dependence than the first one. It must be noted that both the network and the visa variable have lower coeficients in absolute levels than the baseline specification although the diferences are not statistically significant.

When we turn to specifications (3) and (4) in Table 5, we are focusing on low-skill migration. Again, specification (3), without origin-nest fixed efects, has problems of crosssectional dependence since the CD test rejects the null with a value of 9.40. Specification (4) does not have this problem since the statistic is -0.61 and we cannot reject the cross-sectional independence of the residuals (p-value of 0.543). The bias induced by multilateral resistance to migration on low-skill flows seems to be of the same nature as the one we observed in the baseline: lower coeficient on networks and larger on the visa requirement variable in absolute levels. However, it is interesting to note that the absolute values of both coeficients are larger than those observed for high-skill migration flows. This is consistent with the idea that low-skill migration flows might be more sensitive to changes in the costs of migration than high-skill migration flows.⁷⁰

⁶⁸This specification omits the Schengen variable, as the restriction of the sample leaves us with no variability in the data to identify its efect.

⁶⁹This suggests that the disaggregation of migration flows by skill level does not sufice to remove the heterogeneity across potential migrants that induces a correlation in the stochastic component of utility.

It is useful to compare the diferent sensitivity of migration flows by skill level to networks and migration policies by looking again at the implied elasticities according to a RUM model. This is done in Table 6, based in specifications (2) and (4) from Table 5. We can see that the bounds for the direct elasticity of bilateral migration flows with respect to bilateral networks difer between 0.40 to 0.50 for high-skill flows and between 0.50 and 0.61 for lowskill flows. For the cross elasticities, the diferences are smaller: between -0.10 and 0.00 for high-skill flows and between -0.11 and 0.00 for low-skill flows. In the case of the direct efects of bilateral visas on migration flows, the bounds are between -0.42 and -0.35 for high-skill flows but they go up to between -0.50 and -0.42 for low-skill flows. Correspondingly, the externality efect of the visa requirement is also larger for low-skill flows, between 3 and 19 percent, compared with the interval for high-skill flows, between 2 and 14 percent.

6 Concluding remarks

The migration of people across borders can be severely limited by the policies adopted at destination. Our paper provides a contribution to the understanding of the influence exerted by bilateral visa policies on international migration flows, which can be identified only when the confounding efect due to multilateral resistance to migration is adequately controlled for. The prevailing visa regime significantly contributes to determine the height of the “clif at the border” (Pritchett, 2009), and a change in the requirements for non-immigrant admission can influence the scale of migration flows directed both to the country changing its policy

⁷⁰These findings are confirmed when we disaggregate the bilateral migration rates by skill level and by gender; the visa efect for both genders is larger in magnitude for low- than for high-skilled individuals, and slightly larger for men than for women. Results are available from the authors upon request.

and to other destinations.

The estimation of the determinants of international migration on aggregate data does not allow us to recover the structural parameters of the underlying theoretical model, and this creates an unavoidable uncertainty on the estimated direct and indirect efect of the visa policy. Our estimates entail that, on average, the introduction of a visa requirement reduces direct bilateral flows between 40 and 47 percent, while increasing the flows toward other destinations between 3 and 17 percent. The uncertainty on the true size of the efect notwithstanding, these figures are strongly suggestive of the relevance of the legal framework for non-immigrant admission in shaping the scale and direction of international migration flows.

These results confirm and extend the findings in Bertoli and Fernández-Huertas Moraga (2013), and are based on an estimation technique with minimal data requirements, which is well-suited for most of the existing international migration datasets. Regrettably, a binding constraint upon further applications and extensions of the proposed econometric approach is currently represented by the scarcity of longitudinal data on bilateral immigration policies. The International Migration Policy and Law Analysis, IMPALA, and the Determinants of International Migration, DEMIG, projects can fill this gap, allowing to identify the efects of the “clif at the border” upon migration flows out of changes in bilateral policies over time.⁷¹

⁷¹“The IMPALA database is a collaborative project, bringing together social science and legal researchers from Harvard University, the University of Luxembourg, the University of Amsterdam, the London School of Economics, and the University of Sydney” (source: http://projects.iq.harvard.edu/impala, accessed on March 13, 2012); the DEMIG project is conducted at the International Migration Institute, University of Oxford.

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A Direct and indirect efects of visas on migration flows

Let represent the estimated value of the deterministic component of location-specific utility, and and represent the corresponding values when a visa requirement is imposed from country k upon country and when a visa waiver is granted. The ratio between the size of the bilateral migration flow conditional upon and the size of the flow conditional upon measures the efect of the introduction of a visa requirement by country k on . Similarly, we can define as the impact on due to the imposition of a visa requirement by country k upon the citizens of country j.

From (4), we have that:⁷²

\[\widehat {v} _ {k j k} = e ^ {\widehat {\beta_ {1} / \tau}} \left[ \frac {\sum_ {l \in b (k) / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {0} / \tau}}}{\sum_ {l \in b (k) / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {1} / \tau}}} \right] ^ {1 - \tau} \left[ \frac {\sum_ {l \in D / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {0} / \tau}}}{\sum_ {l \in D / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {1} / \tau}}} \right] ^ {\tau}\]

, which is monotonic in for any given estimate of the vector is equal to a weighted geometric average of the efect of the introduction of a visa requirement when converges to 0 and when . When converges to converges to:

\[\widehat {v} _ {k j k} | _ {\tau = 0} = e ^ {\widehat {\beta_ {1} / \tau}} \frac {\sum_ {l \in b (k) / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {0} / \tau}}}{\sum_ {l \in b (k) / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {1} / \tau}}}\tag{A.1}\]

When , this becomes:

\[\widehat {v} _ {k j k} | _ {\tau = 1} = e ^ {\widehat {\beta_ {1} / \tau}} \frac {\sum_ {l \in D / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {0} / \tau}}}{\sum_ {l \in D / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {1} / \tau}}}\tag{A.2}\]

If , then the efect is larger in magnitude when converges to zero (upper bound) than when (lower bound).⁷³ With respect to the efect due to the introduction of a visa requirement by another country l upon , we have that

\[\widehat {v} _ {k j l} \in \left[ \frac {\sum_ {l \in D / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {0} / \tau}}}{\sum_ {l \in D / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {1} / \tau}}}, \frac {\sum_ {l \in b (k) / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {0} / \tau}}}{\sum_ {l \in b (k) / \{k \}} e ^ {\widehat {V _ {j l} / \tau}} + e ^ {\widehat {V _ {j k} ^ {1} / \tau}}}\right)\tag{A.3}\]

β₁

vkjk − 1.

⁷²Without loss of generality, we denote with the parameter in (2) associated to the variable denoting the bilateral visa policy.

⁷³The percentage change induced by the introduction of a visa requirement is simply vbkjk ⁻ 1.

B Endogeneity of networks

An additional concern with the estimation of the determinants of migration flows is that of the endogeneity of migration networks. Factors that generated the networks up to 1990, such as migration flows between 1980 and 1990, are likely to be correlated with the determinants of 1990-2000 migration flows. To address this concern, Beine, Docquier, and Ozden (2011) applied two-stage least squares by instrumenting the size of migration networks in 1990 with old bilateral guest worker agreements and diferent proxies for the networks in 1960, which they did not observe. We have the advantage that a new dataset, created by Ozden, Parsons, Schif, and Walmsley (2011), has come out, which provides us with more precise estimates of the size of the networks in 1960. Thus, we use the networks in 1960 as an instrument for the networks in 1990. We resort to two-stage residual inclusion,⁷⁴ given that the Poisson model is non-linear and 2SPS would generally be inconsistent (Terza, Basu, and Rathouz, 2008).

The results are presented in Table B.1 for all the correct specifications discussed in the paper.⁷⁵ The first stage is very strong, with the size of networks in 1960 having substantial explanatory power over the 1990 variable (the correlation between the two variables is 0.76 in the full sample). Specification (1) reproduces the baseline correct specification (3) from Table 2. The main significant change is the notable increase in the coeficient of migration networks, which suggests that the previous estimate was downward biased. The new coeficient is a strongly significant 0.77, coinciding with the result in Beine, Docquier, and Ozden (2011). A possible interpretation of the direction of the bias, which is also reflected in the negative and significant coeficient for the first stage residuals, relates to return migration: a larger network can be associated with a larger scale of return migration, which influences a dependent variable that captures variation in stocks rather than gross migration flows. As for the visa, the coeficient remains negative and significant at the 90 percent confidence level: -0.62. The rest of specifications are shown for robustness purposes and carry exactly the same message: there is some downward bias on the networks coeficient in the baseline whereas the visa coeficient is virtually unafected although the larger standard errors make it marginally significant. None of the specifications rejects the null of cross-sectional independence in the residuals.

⁷⁴Recent applications of the 2SRI estimator within the migration literature can be found in Beine, Lodigiani, and Vermeulen (2012), Marchetta (2012) and Bertoli and Marchetta (2012).

⁷⁵We present bootstrapped standard errors after 1,000 replications to account for the two-step estimation.

Table 1: Descriptive statistics

Sources: Authors’ elaboration on Docquier, Lowell, and Marfouk (2009) for flows and migration networks in 1990; Ozden, Parsons, Schif, and Walmsley (2011) for migration networks in 1960; Neumayer (2006) for the visa requirement, and Mayer and Zignago (2011) for the rest of the variables.

Table 2: Determinants of migration flows (1990-2000)

Note: standard errors in brackets; *** significant at the 99 percent level, ** significant at the 95 percent level, * significant at the 90 percent level. The dependent variable in specifications (2)-(3) is equal to the maximum between the variation in stocks and zero; standard errors are robust in specifications (1) to (3).

Table 3: Direct and indirect elasticities of networks and visa

Table 4: Determinants of migration flows (1990-2000), diferent samples

Note: standard errors in brackets; *** significant at the 99 percent level, ** significant at the 95 percent level, * significant at the 90 percent level. Specifications (1) and (2) are estimated on a sample restricted to origin countries with a population of at least 1 million; specifications (3) and (4) are estimated on a sample that excludes high-income OECD origin countries. The dependent variable is equal to the maximum between the variation in stocks and zero; standard errors are robust.

Table 5: Determinants of migration flows by skill level (1990-2000)

Note: standard errors in brackets; *** significant at the 99 percent level, ** significant at the 95 percent level, * significant at the 90 percent level. The dependent variable in specifications (1) and (2) refers to migration flows that are tertiary educated in Docquier, Lowell, and Marfouk (2009); specifications (3) and (4) refer to migration flows that are primary and secondary educated. The dependent variable is equal to the maximum between the variation in stocks and zero; standard errors are robust.

Table 6: Direct and indirect elasticities of networks and visa by skill level

Note: standard deviations in parentheses. The bounds correspond to averages, weighted by population at origin, over equations (9), (10) and (A.1)- (A.3) based on the estimates in specifications (2) and (4) in Table 5.

Table B.1: Determinants of migration flows (1990-2000), two-stage residual inclusion

Note: bootstrapped standard errors after 1,000 replications in brackets; *** significant at the 99 percent level, ** significant at the 95 percent level, * significant at the 90 percent level, ^a test that the coeficient is positive p-value = 0.115, ^b test that the coeficient is positive p-value = 0.100. Specification (1) as specification (3) in Table 2; specifications (2) and (3) and specifications (2) and (4) in Table 4; specifications (4) and (5) as specifications (2) and (4) in Table 5. The dependent variable is equal to the maximum between the variation in stocks and zero; the excluded instrument is the natural logarithm of one plus the size of migration networks in 1960 (see Table 1).

Figure 1: Distribution of the countries of origin by visa regime Source: authors’ elaboration on Neumayer (2006).

Figure 2: Bounds for the direct elasticity of migration flows with respect to networks Note: see Table 3 for the average values.

Figure 3: Bounds for the indirect elasticity of migration flows with respect to networks Note: see Table 3 for the average values.

Figure 4: Bounds for the direct efect of the visa requirement on migration flows Note: see Table 3 for the average values.

Figure 5: Bounds for the indirect efect of the visa requirement on migration flows

Note: see Table 3 for the average values.

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